Question: $A$ $B$ $C$ If: $ AC = 104$, $ BC = 5x + 5$, and $ AB = 5x + 9$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {5x + 9} + {5x + 5} = {104}$ Combine like terms: $ 10x + 14 = {104}$ Subtract $14$ from both sides: $ 10x = 90$ Divide both sides by $10$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 5({9}) + 5$ Simplify: $ {BC = 45 + 5}$ Simplify to find ${BC}$ : $ {BC = 50}$